oreDiv — Mathlib

English

For a pair (a,b), its order equals the least common multiple of the orders of a and b.

Русский

Порядок пары (a,b) равен наименьшему общему кратному порядков a и b.

LaTeX

$$orderOf (a,b) = \operatorname{lcm}(orderOf(a), orderOf(b))$$

Lean4

/-- The division in the Ore localization `X[S⁻¹]`, as a fraction of an element of `X` and `S`. -/
@[to_additive /-- The subtraction in the Ore localization,
    as a difference of an element of `X` and `S`. -/
    ]
def oreDiv (r : X) (s : S) : X[S⁻¹] :=
  Quotient.mk' (r, s)

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